...
I think the ability to consider additional operation like contraction does not arise from
and the fact that we are talking about
, but because our present representation comprises not ordinary matrices, but ones that portray (0, 2) tensors. So all the properties we can use to reduce them are those of such tensors; contraction can always be done. The problem is what property the contraction does make use of.
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Am I correct?
Consider orthogonal transformations where
or
(summation convention over repeated indices is assumed here).
Now
using the above condition. Therefore the trace is invariant because of the above condition.
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